Rotating Elliptical Parallel-Plate Capacitor and a Transient Electric Circuit

We consider a pair of identical elliptical plates and orient them at an arbitrary angle about their common axis through the centers, and perpendicular to the plates. In terms of the dimensions of the ellipse and their angular orientation we derive an analytic expression for the overlapping area. We then express the orientation angle as a function of time. For at least two mechanical rotational modes, either a rotation with a constant pace or a rotation with a uniform angular acceleration we express the overlapping area as a continuous function of time. We then assume the elliptical plates are made of metals and that the overlaid plates are separated by a gap; the assembly becomes a parallel-plate capacitor. We adjust the separation gap between the plates so that the fringe effects are ignored. We insert our designed time-dependent capacitor in series with an ohmic resistor and analyze the charging and discharging DC driven electrical characteristic signals of the resulting RC(t) circuit.